Controlling your dragon is easy but it may take you a few games before you get the hang of it. To move your dragon in any direction you simply have to swipe anywhere on the screen in the direction you want it to go. To instantly increase the speed and power of your dragon you just need to hold on the screen with two fingers. That's basically all there is to it as you explore the map trying to survive.
The most important thing you need to take into a account as you move your dragon around the screen during any stage of the game is its size as this will determine the problems besides the enemies you will encounter and have to deal with. Also at the start of the game your movement will be restricted as there will be areas you will not be able to move into until they have been unlocked.